Question to Find Unknown value of the side of a Triangle

Topic : Sine Rule

Question : Find length of side x of ∆ABC if C 28º and side AB =15m and side AC is same as AC

Solution :

AB = AC = 15m (given)
So ∟C = ∟B (because angle opposite to equal sides of a triangle are equal)

So ∟C = ∟B = 28º
According to Sum of angles of triangle property
∟A + ∟B + ∟C = 180º
∟A + 28º + 28º = 180º
∟A + 56º = 180º
∟A = 180º - 56º
∟A = 124º

According Sine Law

Sin A / BC = Sine B / AC = Sine C / AB

Sin 124º / x = Sin 28º / 15 = Sin 28º / 15
Consider Sin 124º / x = Sin 28º / 15

On substituting values, 0.829 / x = 0.407 / 15

0.829 * 15 = x * 0.407
12.435 = 0.407*x
Divide both side by 0.407

x = 30.55m